Go to poll_js macro and replace this line " if (!<n.poll_visitor_can_vote/>) " with this " if (!<n.visitor.can_create_poll_in.page_node/> ) ". In this way, only those who can create polls will be able to vote.
The beginning of your macro will be like this:
<override_macro name="poll_js" requires="servlet">
<n.comment.>
This is the javascript code that will update the poll controls and make them available to the users.
</n.comment.>
<n.param_loop. param="poll_node_id">
<n.get_node_from_id. node_id="[n.current_parameter_value/]">
<n.set_local_node.this_node />
<n.if.visitor.is_registered>
<then>
<n.poll_option_list.loop.>
var input = '<n.local_node.poll_vote_input_field field_id="option[n.option_id/]" index="[n.current_index/]"/>';
$('#poll-option-input<n.option_id/>').html(input);
</n.poll_option_list.loop.>
<n.if.poll_has_ended>
<then>
var input = '<t>This poll is closed.</t>';
</then>
<else>
var txt_vote = "<t>Vote</t>";
var input = '<input type="submit" value="' + txt_vote + '"/>';
if (!<n.visitor.can_create_poll_in.page_node/> )
input = '<input type="submit" value="' + txt_vote + '" disabled="true"/>';
</else>
/(...)